# John H. Conway

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**John Horton Conway**,

a British mathematician and Professor Emeritus at Princeton University ^{[3]}. His research interests include the theory of finite groups, knot theory, number theory, coding theory ^{[4]} and quantum physics. He is best known for the invention of the Game of Life ^{[5]}, and for the co-development of combinatorial game theory ^{[6]} along with a remarkable new way to construct numbers as introduced in his 1976 book *On Numbers and Games*. His surreal numbers were subject of a mathematical novel by Donald Knuth ^{[7]} .

## Contents

# Winning Ways

Winning Ways for your Mathematical Plays by Elwyn Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games, first published 1982 in two volumes, second edition published in four volumes from 2001 until 2004.

# Selected Publications

^{[8]} ^{[9]}

## 1970 ...

- John H. Conway (
**1971**).*Regular Algebra and Finite Machines*. Chapman and Hall, London - John H. Conway (
**1976**).*On Numbers and Games*. Academic Press - John H. Conway, Vera Pless, Neil Sloane (
**1979**).*Self-dual codes over GF(3) and GF(4) of length not exceeding 16*. IEEE Transactions on Information Theory, Vol. 25, No. 3^{[10]}^{[11]} - John H. Conway, Simon P. Norton (
**1979**).*Monstrous Moonshine*. Bulletin of the London Mathematical Society, Vol. 11, 308–339

## 1980 ...

- John H. Conway (
**1980**).*On the Enumeration of Self-Dual Codes*. Journal of Combinatorial Theory, Series A, Vol. 28 - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**1982**).*Winning Ways for your Mathematical Plays*. Vol. 1, 1st edition, Academic Press - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**1982**).*Winning Ways for your Mathematical Plays*. Vol. 2, 1st edition, Academic Press - John H. Conway, Neil Sloane (
**1988**).*Sphere Packing, Lattices and Groups*. Springer

## 1990 ...

- Richard K. Guy, John H. Conway, Elwyn Berlekamp, Vera Pless, Aviezri Fraenkel, Richard J. Nowakowski (
**1991**).*Combinatorial Games*. Proceedings of Symposia in Applied Mathematics, No. 43 - John H. Conway (
**1996**).*The Angel Problem*. in Richard J. Nowakowski (ed) (**1996**).*Games of No Chance*, MSRI Publications Volume 29, Cambridge University Press, Papers from the Combinatorial Games Workshop held in Berkeley, CA, July 11–21, 1994^{[12]} - John H. Conway, Neil Sloane (
**1998**).*Sphere Packing, Lattices and Groups*. 3rd edition, Springer

## 2000 ...

- John H. Conway (
**2001**).*On Numbers and Games*. 2nd edition, A K Peters Ltd. - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**2001**).*Winning Ways for your Mathematical Plays*. Vol. 1, 2nd edition, A K Peters Ltd. - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**2003**).*Winning Ways for your Mathematical Plays*. Vol. 2, 2nd edition, A K Peters Ltd. - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**2003**).*Winning Ways for your Mathematical Plays*. Vol. 3, A K Peters Ltd. - Elwyn Berlekamp, John H. Conway, Richard K. Guy (
**2004**).*Winning Ways for your Mathematical Plays*. Vol. 4, A K Peters Ltd. - John H. Conway, Noam D. Elkies, Jeremy L. Martin (
**2006**).*The Mathieu Group M 12 and Its Pseudogroup Extension M 13*. Experimental Mathematics, Vol. 15, No. 2^{[13]}^{[14]} - John H. Conway, Simon B. Kochen (
**2006**).*The Free Will Theorem*. arXiv:quant-ph/0604079 - John H. Conway, Simon B. Kochen (
**2007**).*Thou Shalt Not Clone One Bit!*. arXiv:0711.2310 - John H. Conway, Simon B. Kochen (
**2008**).*The Strong Free Will Theorem*. arXiv:0807.3286

## 2010 ...

- William Cavendish, John H. Conway (
**2010**).*Symmetrically Bordered Surfaces*. The American Mathematical Monthly 117, pdf - John H. Conway (
**2013**).*On Unsettleable Arithmetical Problems*. The American Mathematical Monthly 120 - Siobhan Roberts (
**2015**).*Genius at Play - The Curious Mind of John Horton Conway*. Bloomsbury Publishing, YouTube Video

# External Links

## John H. Conway

- John Conway | Department of Mathematics
- John Horton Conway from Wikipedia
- The Mathematics Genealogy Project - John Conway
- Conway biography - MacTutor
- John Conway - АдептИС: Под знаком Leonardo da Vinci (Russian)

## Topics

- Angel problem from Wikipedia
- Conway's Game of Life from Wikipedia
- Conway group from Wikipedia
- Conway notation (knot theory) from Wikipedia
- Conway polyhedron notation from Wikipedia
- Doomsday rule from Wikipedia
- Free will theorem from Wikipedia
- Hackenbush from Wikipedia
- Monstrous moonshine from Wikipedia

## Videos

- Inventing Game of Life - Numberphile, YouTube Video

- Stanley Clarke Band - Life Is Just a Game, North Sea Jazz Festival 1981, YouTube Video

# References

- ↑ John Conway - АдептИС: Под знаком Leonardo da Vinci
- ↑ Conway biography - MacTutor
- ↑ John Conway | Department of Mathematics
- ↑ John Horton Conway from Wikipedia
- ↑ Martin Gardner (
**1970**).*Mathematical Games - The fantastic combinations of John Conway's new solitaire game "life"*. Scientific American, Vol. 223, pp. 120-123. - ↑ Richard J. Nowakowski (
**2009**).*The History of Combinatorial Game Theory*. Dalhousie University, pdf - ↑ Donald Knuth (
**1974**).*Surreal Numbers - How two ex-students turned on to pure mathematics and found total happiness*. Addison-Wesley - ↑ dblp: John H. Conway
- ↑ John H. Conway - Bibliography (pdf)
- ↑ Dual code from Wikipedia
- ↑ Finite field from Wikipedia
- ↑ Angel problem from Wikipedia
- ↑ Mathieu group M12 from Wikipedia
- ↑ Mathieu groupoid from Wikipedia